Behaviour of solutions of quasilinear elliptical equations of the second order in nonrestricted regions

Abstract

Analogues of the well known in the theory of analytic functions Phragmén — Lindelöff theorem are formulated for the solutions of a wide class of quasilinear equations of elliptic type. Examples are given which illustrate the sharpness of the obtained results for solutions of equations of the form div (|∇и|^α-2∇и) = f (х, и), where the function f(x, u) is locally bounded in ℝⁿ⁺¹,

f (х, 0) = 0, uf (х, и) ≥ а|и|^1+q, а > 0, α > 1, α – 1 > q ≥ 0, n ≥ 2.